Google Scholar and the Turner College

Every few months Turner Business posts about the Google Scholar citations to the research of Turner College business faculty. According to the most recent data, research by the 11 corps of instruction faculty in the Department of Accounting and Finance, which includes economics, has so far garnered 7,275 Google Scholar citations, for an average of 661.4 Google Scholar citations per faculty. Additionally, research by the 15 corps of instruction faculty in the Department of Management and Marketing, which includes management information systems, has to date garnered 12,169 Google Scholar citations, for an average of 811.3 Google Scholar citations per faculty. Thus, research by all 26 corps of instruction business faculty has earned 19,444 Google Scholar citations, for an average of 747.8 Google Scholar citations per faculty.

     Because Turner Business likes to provide all sorts of new information, this post takes the analysis a bit further. Developed by American economist Max Lorenz, the Lorenz Curve is a graphical representation of a distribution of some sort, usually income or wealth. Most often used to discuss income or wealth inequality, the horizontal axis measures the cumulative percent of some population or group while the vertical axis measures the cumulative percent of some variable, such as income or wealth. In this case that variable is Google Scholar citations, and the group is an academic department. If, starting with the prof with the fewest citations and moving to the prof with the most, Google Scholar citations are evenly spread across the group, the actual distribution is a 45-degree line like that shown below labelled "Perfect Equality Line." The more uneven the spread, the further to the right of that line lies the actual distribution. Beginning where we left off above, the actual distribution of Google Scholar citations from the Department of Management and Marketing is represented by the orange curve in the diagram below. As can be seen, it is generally about halfway between the perfect equality line and the horizontal and vertical (on the right) axes, meaning that the Google Scholar citations spread for the Department of Management and Marketing is fairly uneven.

 

Next, we return to the Department of Accounting and Finance. The actual distribution of Google Scholar citations for this unit is shown as the green curve in the diagram below. Visually, it appears to be further to the right of the perfect equality line than the Turner College's other business department. In fact, if the orange distribution above is about halfway between the equality line and the axes to the right, then the green distribution below appears to be about halfway between the orange distribution above and the axes to the right.

Fortunately for an analysis like this, Italian statistician Corrado Gini envisioned a mathematical way to compare the inequality of separate distributions. Using his approach, we can divide the size of area between the perfect equality line and an actual distribution by the size of the entire area underneath the perfect equality line. If the actual distribution is spread evenly, then that distribution will be represented by the perfect equality line and the Gini coefficient will be equal to 0. On the other hand, if the actual distribution lies along the axes (right) of the diagram (i.e., the most unequal distribution), the Gini coefficient will be equal to 1. According to our analysis, the Gini coefficient for the Department of Management and Marketing's Google Scholar citations distribution is 0.552. So, the visual inspection described above suggesting that the orange curve lies about halfway between the perfect equality line and the axes on the right is quite close to the true location. Or analysis also indicates that the Gini coefficient for the Department of Accounting and Finance is 0.778, which is a bit larger than the prior one and supports our visual inspection above suggesting that the green distribution lies about halfway between the orange distribution and the axes on the right.